Question

Solve the inequality | x + 5/3 | -3 > 6

Answer 1

The solution to the inequality is x > 22/3 or x < -32/3

Step-by-step explanation

The given inequality is:

`|x+(5)/(3)|-3>6`

The inequality can be solved as follows:

`\begin{gathered} |x+(5)/(3)|-3>6 \\ \\ Take-3\text{ }to\text{ }the\text{ }other\text{ }side\text{ }of\text{ }the\text{ }inequality\text{ }sign \\ \\ |x+(5)/(3)|>6+3 \\ \\ |x+(5)/(3)|>9 \end{gathered}`

Now, split the absolute value into two inequalities, for case > 9 or < -9

`\begin{gathered} x+(5)/(3)>9\text{ }or\text{ }x+(5)/(3)<-9 \\ \\ x>9-(5)/(3)\text{ }or\text{ }x<-9-(5)/(3) \\ \\ x\gt(27-5)/(3)\text{ }or\text{ }x\lt(-27-5)/(3) \\ \\ x>(22)/(3)\text{ }or\text{ }x<(-32)/(3) \end{gathered}`

Hence the solution to the inequality | x + 5/3 | -3 > 6 is x > 22/3 or x < -32/3